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Multi-layered diffusive convection. Part 2. Dynamics of layer evolution

Published online by Cambridge University Press:  26 March 2010

TAKASHI NOGUCHI  and
HIROSHI NIINO
TAKASHI NOGUCHI*
Affiliation:
Ocean Research Institute, The University of Tokyo, Nakano, Tokyo 164-8639, Japan
HIROSHI NIINO
Affiliation:
Ocean Research Institute, The University of Tokyo, Nakano, Tokyo 164-8639, Japan
*
†Present address: Department of Aeronautics and Astronautics, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto 606-8501, Japan. Email address for correspondence: [email protected]
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Abstract

Evolution of layers in an unbounded diffusively stratified two-component fluid and its dynamics are studied by means of a direct numerical simulation (DNS) and an analytical model. The numerical simulation shows that the layers grow by repeating mergings with the neighbouring layers. By analysing the results of the numerical simulation, the mechanism of the merging is examined in detail. Two modes of merging are found to exist: one is the layer vanishing mode and the other is the interface vanishing mode. The vanishings of layers and interfaces are caused by turbulent entrainment at the interfaces. Based on the analysis of the numerical model, a one-dimensional asymmetric entrainment model is proposed. In the model, each layer is assumed to interact with its neighbouring layers through simplified convective entrainment laws. The model is applied to two simple configurations of layers and is proved to reproduce the layer evolutions found in the DNS successfully.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 651 , 25 May 2010 , pp. 465 - 481
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Huppert, H. E. 1971 On the stability of a series of double-diffusive layers. Deep Sea Res. 18, 1005–1021.Google Scholar
Huppert, H. E. & Linden, P. F. 1979 On heating a stable salinity gradient from below. J. Fluid Mech. 95, 431–464.CrossRefGoogle Scholar
Huppert, H. E. & Turner, J. S. 1981 A laboratory model of a replenished magma chamber. Earth Planet. Sci. Lett. 54, 144–172.CrossRefGoogle Scholar
Kelley, D. E., Fernando, H. J. S., Gargett, A. E., Tanny, J. & Özsoy, E. 2003 The diffusive regime of double-diffusive convection. Prog. Oceanogr. 56, 461–481.CrossRefGoogle Scholar
Linden, P. F. 1976 The formation and destruction of fine-structure by double diffusive processes. Deep Sea Res. 23, 895–908.Google Scholar
Linden, P. F. & Shirtcliffe, T. G. L. 1978 The diffusive interface in double-diffusive convection. J. Fluid Mech. 87, 417–432.CrossRefGoogle Scholar
Moeng, C.-H. & Rotunno, R. 1990 Vertical-velocity skewness in the buoyancy-driven boundary layer. J. Atmos. Sci. 47, 1149–1162.2.0.CO;2>CrossRefGoogle Scholar
Neshyba, S., Neal, V. T. & Denner, W. 1971 Temperature and conductivity measurements under upper Ice Island T-3. J. Geophys. Res. 76, 8107–8120.CrossRefGoogle Scholar
Noguchi, T. & Niino, H. 2010 Multi-layered diffusive convection. Part 1. Spontaneous layer formation. J. Fluid Mech. doi:10.1017/S0022112009994150.CrossRefGoogle Scholar
Schmitt, R. W. 1994 Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26, 255–285.CrossRefGoogle Scholar
Shirtcliffe, T. G. L. 1969 An experimental investigation of thermosolutal convection at marginal stability. J. Fluid Mech. 35, 677–688.CrossRefGoogle Scholar
Stamp, A. P., Hughes, G. O., Nokes, R. I. & Griffiths, R. W. 1998 The coupling of waves and convection. J. Fluid Mech. 372, 231–271.CrossRefGoogle Scholar
Turner, J. S. 1965 The coupled turbulent transports of salt and heat across a sharp density interface. Intl J. Heat Mass Trans. 8, 759–767.CrossRefGoogle Scholar
Zangrando, F. & Fernando, H. J. S. 1991 A predictive model for the migration of double-diffusive interfaces. J. Solar Energy Engng 113, 59–65.CrossRefGoogle Scholar
Zimmerman, W. B. & Rees, J. M. 2007 Rollover instability due to double diffusion in a stably stratified cylindrical tank. Phys. Fluids 19, 123604.CrossRefGoogle Scholar